Question: Solve for $x$ and $y$ using elimination. ${-2x-3y = -29}$ ${5x+3y = 50}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $3x = 21$ $\dfrac{3x}{{3}} = \dfrac{21}{{3}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-2x-3y = -29}\thinspace$ to find $y$ ${-2}{(7)}{ - 3y = -29}$ $-14-3y = -29$ $-14{+14} - 3y = -29{+14}$ $-3y = -15$ $\dfrac{-3y}{{-3}} = \dfrac{-15}{{-3}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {5x+3y = 50}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ + 3y = 50}$ ${y = 5}$